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Recent developments in the theory of Borel reducibility

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Hjorth G., Kechris A.

Fundamenta Mathematicae

2001

tom 170

nr 1-2

21-52

Let E₀ be the Vitali equivalence relation and E₃ the product of countably many copies of E₀. Two new dichotomy theorems for Borel equivalence relations are proved. First, for any Borel equivalence relation E that is (Borel) reducible to E₃, either E is reducible to E₀ or else E₃ is reducible to E. Second, if E is a Borel equivalence relation induced by a Borel action of a closed subgroup of the infinite symmetric group that admits an invariant metric, then either E is reducible to a countable Borel equivalence relation or else E₃ is reducible to E. We also survey a number of results and conjectures concerning the global structure of reducibility on Borel equivalence relations.

Dynamical properties of the automorphism groups of the random poset and random distributive lattice

100%

Kechris A., Sokić M.

Fundamenta Mathematicae

2012

tom 218

nr 1

69-94

A method is developed for proving non-amenability of certain automorphism groups of countable structures and is used to show that the automorphism groups of the random poset and random distributive lattice are not amenable. The universal minimal flow of the automorphism group of the random distributive lattice is computed as a canonical space of linear orderings but it is also shown that the class of finite distributive lattices does not admit hereditary order expansions with the Amalgamation Property.

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Kechris A.

1 Hjorth G.

1 Sokić M.

1 2012

1 2001

Wyniki wyszukiwania

Recent developments in the theory of Borel reducibility

Dynamical properties of the automorphism groups of the random poset and random distributive lattice